Electrostatic environment and Majorana bound states in full-shell topological insulator nanowires

TL;DR

This paper investigates how electrostatic effects influence the emergence of Majorana zero modes in superconductor-topological insulator nanowires, revealing conditions for their realization despite complex electrostatic environments.

Contribution

It systematically analyzes the electrostatic environment's impact on topological properties and Majorana modes in TI nanowires using Schrödinger-Poisson calculations, providing practical insights.

Findings

Band bending causes Fermi level shifts and coexistence of surface and bulk states.

Superconducting gap suppression depends on magnetic flux and nanowire radius.

Majorana zero modes can be achieved over a wide parameter range around one flux quantum.

Abstract

The combination of a superconductor (SC) and a topological insulator (TI) nanowire was proposed as a potential candidate for realizing Majorana zero modes (MZMs). In this study, we adopt the Schr\"odinger-Poisson formalism to incorporate the electrostatic environment inside the nanowire and systematically explore its topological properties. Our calculations reveal that the proximity to the SC induces a band bending effect, leading to a non-uniform potential across the TI nanowire. As a consequence, there is an upward shift of the Fermi level within the conduction band. This gives rise to the coexistence of surface and bulk states, localized in an accumulation layer adjacent to the TI-SC interface. When magnetic flux is applied, these occupied states have different flux-penetration areas, suppressing the superconducting gap. However, this impact can be mitigated by increasing the radius of the nanowire. Finally, We demonstrate that MZMs can be achieved across a wide range of parameters centered around one applied flux quantum, $\phi_0 = h/2e$. Within this regime, MZMs can be realized even in the presence of conduction bands, which are not affected by the band bending effect. These findings provide valuable insights into the practical realization of MZMs in TI nanowire-based devices, especially in the presence of a complicated electrostatic environment.